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This article investigates the attitude tracking control problem for a class of flexible spacecraft with a redundant four reaction wheels' setting. In this study, inertia uncertainties, external disturbance, wheel torque saturation, and configuration misalignment are taken into account simultaneously. Two types of sliding mode controllers are presented to solve this design problem. First, supposing the norm upper bound of external disturbances, bounds of inertia, and input uncertainties are available, a terminal sliding mode attitude tracking control strategy is developed, where the controller and steering laws are synthesized together. Second, supposing these norm upper bounds are unavailable, an adaptive control law is designed to cope with attitude tracking problem. Under both control schemes, the system trajectory can be ensured to arrive on the specified sliding surface in finite time. Finally, an illustrative example is given to verify the effectiveness of the proposed attitude tracking control methodologies.

Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study investigates the dynamics of 1-dof and 2-dof NES with nonlinear damping and combined stiffness connected to a linear oscillator. For the system of 1-dof NES, a truncation damping and failure frequency are revealed through bifurcation analysis using the complex variable averaging method. The frequency detuning interval for the existence of the strongly modulated response (SMR) is also reported. For the system of 2-dof NES, it is reported in a similar bifurcation analysis that the mass distribution between NES affects the maximum value of saddle-node bifurcation. To obtain the periodic solution of the 2-dof NES system with the consideration of frequency detuning, the incremental harmonic balance method (IHB) and Floquet theory are employed. The corresponding response regime is obtained by Poincare mapping, it shows that the responses of the linear oscillator and 2-dof NES are not always consistent, and 2-dof NES can generate extra SMR than 1-dof NES. Finally, the vibration suppression effect of the proposed NES with nonlinear damping and combined stiffness is analyzed and verified by the energy spectrum, and it also shows that the 2-dof NES system demonstrates better performance.

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